Nonclassical nonlinear elasticity of crystalline structures

Khandelwal, Aakash; Chakrapani, Sunil Kishore

doi:10.1103/physreve.104.045002

Cited by 4 publications

(1 citation statement)

References 49 publications

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“…However, materials with weak nonlinearity such as metals, plastics, etc., are mostly modeled using a Taylor series approximation of the strain density function. The present study will explore classical nonlinear sources and omit the non-classical case partly due to its complexity and since it has been dealt with elsewhere [42,43]. However, the results from the classical model highlight the necessity to develop a deeper understanding of the non-classical models.…”

Section: Introductionmentioning

confidence: 99%

Analytical Study of Nonlinear Flexural Vibration of a Beam with Geometric, Material and Combined Nonlinearities

Madhuranthakam,

Chakrapani

2024

Vibration

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This article explores the nonlinear vibration of beams with different types of nonlinearities. The beam vibration was modeled using Hamilton’s principle, and the equation of motion was solved using method of multiple time scales. Three models were developed assuming (a) geometric nonlinearity, (b) material nonlinearity and (c) combined geometric and material nonlinearity. The material nonlinearity also included both third and fourth nonlinear elasticity terms. The frequency response equation of these models were further evaluated quantitatively and qualitatively. The models capture the hardening effect, i.e., increase in resonant frequency as a function of forcing amplitude for geometric nonlinearity, and the softening effect, i.e., decrease in resonant frequency for material nonlinearity. The model is applied on the first three bending modes of the cantilever beam. The effect of the fourth-order material nonlinearity was smaller compared to the third-order term in the first mode, whereas it is significantly larger in second and third mode. The combined nonlinearity models shows a discontinuous frequency shift, which was resolved by utilizing a set of transition assumptions. This results in a smooth transition between the material and geometric zones in amplitude. These parametric models allow us to fine tune the nonlinear response of the system by changing the physical properties such as geometry, linear and nonlinear elastic properties.

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Section: Introductionmentioning

confidence: 99%

Analytical Study of Nonlinear Flexural Vibration of a Beam with Geometric, Material and Combined Nonlinearities

Madhuranthakam,

Chakrapani

2024

Vibration

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Revisiting the birth of NaCl crystals using molecular dynamics simulation

Soares

Gonçalves

Horta

et al. 2022

Journal of Molecular Graphics and Modelling

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Non-equilibrium strain induces hysteresis and anisotropy in the quasi-static and dynamic elastic behavior of sandstones: Theory and experiments

Kober

Scalerandi

Zeman

2023

Applied Physics Letters

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Materials with grain contacts or partially closed cracks exhibit anomalous elastic behavior: hysteresis in quasi-static experiments and slow dynamics in fast dynamic ones. Albeit the behavior in the two cases (which correspond to very different strain ranges) appears different, it should stem from the same physics and, thus, could be modeled by a universal equation of state. We propose a modification of the standard acoustoelastic theory, introducing the concept of conditioning induced non-equilibrium strain, which allows us to predict the evolution of elastic wave velocity in both quasi-static and dynamic ranges, including the velocity anisotropy induced by external uniaxial loading.

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Nonclassical nonlinear elasticity of crystalline structures

Cited by 4 publications

References 49 publications

Analytical Study of Nonlinear Flexural Vibration of a Beam with Geometric, Material and Combined Nonlinearities

Analytical Study of Nonlinear Flexural Vibration of a Beam with Geometric, Material and Combined Nonlinearities

Revisiting the birth of NaCl crystals using molecular dynamics simulation

Non-equilibrium strain induces hysteresis and anisotropy in the quasi-static and dynamic elastic behavior of sandstones: Theory and experiments

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